Diffusive dynamics of critical fluctuations near the QCD critical point

TL;DR

This paper develops a stochastic fluid dynamical model to describe the non-equilibrium critical fluctuations of net-baryon density near the QCD critical point, highlighting finite size effects and dynamic scaling behaviors.

Contribution

It introduces a nonlinear stochastic diffusion framework incorporating the 3d Ising universality class to analyze critical fluctuations in finite systems.

Findings

Finite size effects cause deviations from equilibrium fluctuation behavior.

Non-Gaussian fluctuations emerge from Gaussian noise due to finite size and conservation laws.

Critical slowing down affects the real-time evolution of fluctuations.

Abstract

A quantitatively reliable theoretical description of the dynamics of fluctuations in non-equilibrium is indispensable in the experimental search for the QCD critical point by means of ultra-relativistic heavy-ion collisions. In this work we consider the fluctuations of the net-baryon density which becomes the slow, critical mode near the critical point. Due to net-baryon number conservation the dynamics is described by the fluid dynamical diffusion equation, which we extend to contain a white noise stochastic current. Including nonlinear couplings from the 3d Ising model universality class in the free energy functional, we solve the fully interacting theory in a finite size system. We observe that purely Gaussian white noise generates non-Gaussian fluctuations, but finite size effects and exact net-baryon number conservation lead to significant deviations from the expected behavior in equilibrated systems. In particular the skewness shows a qualitative deviation from infinite volume expectations. With this benchmark established we study the real-time dynamics of the fluctuations. We recover the expected dynamical scaling behavior and observe retardation effects and the impact of critical slowing down near the pseudo-critical temperature.